Finite Group Databasebeta

← C2×C3×#4809 #11863651

Subgroups — C2×C3×#4809 #11863651

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C22×C3×Dic12C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic
5C2×C32×#103C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4809C218yesmaximal, direct product factor
9C2×C3×#451—31nomaximal
10C2×#4809C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C2×C3×D3×Q8—24no—
13C2×C3×D3×Q8—22no—
14C2×C3×D3×Q8—24no—
15C2×C3×D3×Q8C2214yes—
16C22×C3×C4×D3—21no—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6—21no—
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C3×#216—24no—
24C2×C3×#216C2214yescomplemented
25C2×C3×(C2×D3)⋊C4—21no—
26C2×C3×C4⋊Dic3—21no—
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×C3×Dic12—24no—
29C2×C3×Dic12C2214yescomplemented
30C3×#897—22no—
31C3×#897C2214yes—
32C32×#103C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yes—
34C3×#810C2214yescomplemented
35C23×C3×Q8—31no—
36C22×D3×Q8C2×C311yescharacteristic
37C22×C3×Q16—31no—
38C22×C3×Q16—31no—
39C2×C3×C22⋊Q8—31no—
40C22×#216C2×C311yescharacteristic, complemented
41C22×Dic12C2×C311yescharacteristic, complemented
42C2×#897C2×C311yescharacteristic
43C3×#451—38no—
44C2×C3×#103—21no—
45C2×C3×#103—31no—
46C2×C3×#103D311yescharacteristic, complemented
47C2×C3×#103C2×C311yescharacteristic, complemented
48C2×C3×C22⋊C8—31no—
49C2×(C2×D3)⋊C8C2×C311yescharacteristic
50C2×#810C2×C311yescharacteristic, complemented
51#4809C2×C318yesdirect product factor
52C23×C3×D3D411yescharacteristic
53C2×C32×Q8—22no—
54C2×C32×Q8—21no—
55C2×C32×Q8D414yes—
56C2×C32×Q8C2312yes—
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C3×D3×Q8—216no—
64C3×D3×Q8—28no—
65C3×D3×Q8—28no—
66C2×C3×C4×D3—28no—
67C2×C3×C4×D3—24no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3D412yes—
71C2×C3×C4×D3C2312yes—
72C2×C3×Dic6—28no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—24no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D414yes—
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2312yes—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C3×#216—28no—
87C3×(C2×D3)⋊C4—24no—
88C3×C4⋊Dic3—24no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91C3×Dic12—28no—
92C2×#451—31noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8—34no—
95C22×C3×Q8—31no—
96C22×C3×Q8—31no—
97C22×C3×Q8—61no—
98C22×C3×Q8—62no—
99C22×C3×Q8—64no—
100C22×C3×Q8—64no—
101C22×C3×Q8C2×D311yescharacteristic
102C22×C3×Q8C22×C311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C2×D3×Q8—24no—
106C2×D3×Q8—22no—
107C2×D3×Q8—24no—
108C2×D3×Q8C22×C314yes—
109C22×C4×D3—21no—
110C22×C4×D3C22×C311yescharacteristic
111C22×Dic6—21no—
112C22×Dic6C22×C311yescharacteristic
113C22×Dic6C22×C311yescharacteristic
114C2×C3×Q16—34no—
115C2×C3×Q16—34no—
116C2×C3×Q16—64no—
117C2×C3×Q16—64no—
118C22×C3×C8—21no—
119C22×C3×C8—31no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C22×C311yescharacteristic
122C3×C22⋊Q8—34no—
123C3×C22⋊Q8—62no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—61no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C22×C311yescharacteristic
128C2×C3×C22⋊C4—61no—
129C2×#216—24no—
130C2×#216C22×C314yescomplemented
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3—21no—
133C22×C3⋊C8C22×C311yescharacteristic
134C2×Dic12—24no—
135C2×Dic12C22×C314yescomplemented
136#897—22no—
137#897C22×C314yes—
138C3×#103—24no—
139C3×#103—34no—
140C3×#103C2×D314yescomplemented
141C3×#103C22×C314yescomplemented
142C3×C22⋊C8—34no—
143(C2×D3)⋊C8C22×C314yes—
144#810C22×C314yescomplemented
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3Q1614yescomplemented
149C22×C3×D3C2×D412yes—
150C32×Q8—24no—
151C32×Q8—22no—
152C32×Q8C2×D414yes—
153C2×C32×C4—24no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—42no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2411yescharacteristic
161C2×C3×Dic3—22no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—42no—
166C2×C3×Dic3C2×D412yes—
167C3×C4×D3—216no—
168C3×C4×D3—24no—
169C3×C4×D3—22no—
170C3×C4×D3—22no—
171C3×Dic6—216no—
172C3×Dic6—24no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C3×Dic6—42no—
177C3×Dic6C2×D414yes—
178C32×C8—22no—
179C3×C3⋊C8—22no—
180C23×Q8—31no—
181C22×Q16—31no—
182C22×Q16—31no—
183C2×C22⋊Q8—31no—
184#451—38no—
185C2×#103—31no—
186C2×#103C3×D311yescharacteristic, complemented
187C2×C22⋊C8—31no—
188C24×C3—31no—
189C23×D3C3×D411yescharacteristic
190C2×C3×Q8—22no—
191C2×C3×Q8—21no—
192C2×C3×Q8—22no—
193C2×C3×Q8—21no—
194C2×C3×Q8—24no—
195C2×C3×Q8—22no—
196C2×C3×Q8—34no—
197C2×C3×Q8—32no—
198C2×C3×Q8—32no—
199C2×C3×Q8—41no—
200C2×C3×Q8—42no—
201C2×C3×Q8—64no—
202C2×C3×Q8—68no—
203C2×C3×Q8—68no—
204C2×C3×Q8—616no—
205C2×C3×Q8—68no—
206C2×C3×Q8—62no—
207C2×C3×Q8—61no—
208C2×C3×Q8—61no—
209C2×C3×Q8—62no—
210C2×C3×Q8—62no—
211C2×C3×Q8D1214yes—
212C2×C3×Q8C3×D414yes—
213C2×C3×Q8C22×D312yes—
214C2×C3×Q8C23×C312yes—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—31no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—41no—
224C22×C3×C4—41no—
225C22×C3×C4—64no—
226C22×C3×C4—68no—
227C22×C3×C4—61no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C23×C311yescharacteristic
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C3×D411yescharacteristic
236D3×Q8—216no—
237D3×Q8—28no—
238D3×Q8—28no—
239C2×C4×D3—28no—
240C2×C4×D3—24no—
241C2×C4×D3—22no—
242C2×C4×D3—22no—
243C2×C4×D3C3×D412yes—
244C2×C4×D3C23×C312yes—
245C2×Dic6—28no—
246C2×Dic6—22no—
247C2×Dic6—21no—
248C2×Dic6—24no—
249C2×Dic6—22no—
250C2×Dic6—22no—
251C2×Dic6—21no—
252C2×Dic6C3×D414yes—
253C2×Dic6C23×C312yes—
254C2×Dic6C23×C312yes—
255C3×Q16—68no—
256C3×Q16—68no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C2×C3×C8—32no—
261C2×C3×C8—42no—
262C2×C3×C8—62no—
263C2×C3×C8C22×D312yes—
264C2×C3×C8C23×C312yes—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—41no—
269C3×C4⋊C4—64no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C23×C312yes—
272C3×C22⋊C4—64no—
273#216—28no—
274(C2×D3)⋊C4—24no—
275C4⋊Dic3—24no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8C23×C312yes—
278Dic12—28no—
279C22×C32#12012yes—
280C22×C32C2×Q1612yes—
281C22×C32#13712yes—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—28no—
286C2×C3×D3C2×Q1614yescomplemented
287C32×C4—24no—
288C32×C4—42no—
289C32×C4#12012yes—
290C32×C4C22×D411yescharacteristic
291C32×C4C22×D411yescharacteristic
292C3×Dic3—22no—
293C3×Dic3—24no—
294C3×Dic3—42no—
295C22×Q8—34no—
296C22×Q8—31no—
297C22×Q8—31no—
298C22×Q8—61no—
299C22×Q8—62no—
300C22×Q8—64no—
301C22×Q8—64no—
302C22×Q8C2×C3×D311yescharacteristic
303C23×C4—31no—
304C23×C4—61no—
305C2×Q16—34no—
306C2×Q16—34no—
307C2×Q16—64no—
308C2×Q16—64no—
309C22×C8—31no—
310C22×C8C2×C3×D311yescharacteristic
311C22⋊Q8—34no—
312C22⋊Q8—62no—
313C2×C4⋊C4—61no—
314C2×C4⋊C4C2×C3×D311yescharacteristic
315C2×C22⋊C4—61no—
316#103—34no—
317#103C2×C3×D314yescomplemented
318C22⋊C8—34no—
319C23×C3—21no—
320C23×C3—34no—
321C23×C3—32no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3D3×D411yescharacteristic
325C23×C3C2×C3×D411yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3C3×Q1614yescomplemented
329C22×D3C2×C3×D412yes—
330C3×Q8—24no—
331C3×Q8—24no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—24no—
335C3×Q8—34no—
336C3×Q8—44no—
337C3×Q8—42no—
338C3×Q8—616no—
339C3×Q8—64no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×Q8—62no—
343C3×Q8—122no—
344C3×Q8C2×D1214yes—
345C3×Q8C2×C3×D414yes—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—32no—
357C2×C3×C4—44no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—616no—
363C2×C3×C4—62no—
364C2×C3×C4—64no—
365C2×C3×C4—62no—
366C2×C3×C4—64no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—82no—
371C2×C3×C4—122no—
372C2×C3×C4C2×D1212yes—
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D412yes—
375C2×C3×C4C2×C3×D412yes—
376C2×C3×C4C2×C3×D411yescharacteristic
377C2×C3×C4C2×C3×D412yes—
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C24×C311yescharacteristic
380C2×Dic3—22no—
381C2×Dic3—24no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—42no—
385C2×Dic3C2×C3×D412yes—
386C4×D3—216no—
387C4×D3—24no—
388C4×D3—22no—
389C4×D3—22no—
390Dic6—216no—
391Dic6—24no—
392Dic6—22no—
393Dic6—22no—
394Dic6—22no—
395Dic6—42no—
396Dic6C2×C3×D414yes—
397C3×C8—22no—
398C3×C8—22no—
399C3×C8—42no—
400C3×C8—62no—
401C3⋊C8—22no—
402C2×C32#45114yescomplemented
403C2×C32C2×#12011yescharacteristic
404C2×C32C22×Q1611yescharacteristic
405C2×C32C2×#13711yescharacteristic
406C3×D3—24no—
407C24—31no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—32no—
411C2×Q8—32no—
412C2×Q8—34no—
413C2×Q8—64no—
414C2×Q8—68no—
415C2×Q8—68no—
416C2×Q8—616no—
417C2×Q8—68no—
418C2×Q8—62no—
419C2×Q8—61no—
420C2×Q8—61no—
421C2×Q8—62no—
422C2×Q8—62no—
423C2×Q8C3×D1214yes—
424C2×Q8C22×C3×D312yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—31no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—64no—
431C22×C4—68no—
432C22×C4—61no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—61no—
436C22×C4C22×C3×D311yescharacteristic
437Q16—68no—
438Q16—68no—
439C2×C8—22no—
440C2×C8—32no—
441C2×C8—62no—
442C2×C8C22×C3×D312yes—
443C4⋊C4—21no—
444C4⋊C4—64no—
445C4⋊C4C22×C3×D312yes—
446C22⋊C4—64no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—34no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—68no—
455C22×C3#88212yes—
456C22×C3#91512yes—
457C22×C3D3×Q1612yes—
458C22×C3C3×#12012yes—
459C22×C3C2×C3×Q1612yes—
460C22×C3C3×#13712yes—
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C22×C3×D411yescharacteristic
463C2×D3—22no—
464C2×D3—28no—
465C2×D3—22no—
466C2×D3C2×C3×Q1614yescomplemented
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—22no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—44no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—62no—
476C3×C4—64no—
477C3×C4—82no—
478C3×C4—122no—
479C3×C4#88212yes—
480C3×C4C3×#12012yes—
481C3×C4C22×D1211yescharacteristic
482C3×C4C2×D3×D411yescharacteristic
483C3×C4C22×C3×D411yescharacteristic
484C3×C4C22×C3×D411yescharacteristic
485Dic3—22no—
486Dic3—24no—
487Dic3—42no—
488C32C2×#45111yescharacteristic, complemented, Sylow
489C23—34no—
490C23—32no—
491C23—62no—
492C23—62no—
493C23C3×D3×D411yescharacteristic
494Q8—24no—
495Q8—22no—
496Q8—34no—
497Q8—616no—
498Q8—64no—
499Q8—62no—
500Q8—62no—
501Q8—62no—
502Q8—122no—
503Q8C2×C3×D1214yes—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—32no—
508C2×C4—42no—
509C2×C4—616no—
510C2×C4—62no—
511C2×C4—64no—
512C2×C4—62no—
513C2×C4—64no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—122no—
518C2×C4C2×C3×D1212yes—
519C2×C4C3×D3×D411yescharacteristic
520C2×C4C3×D3×D412yes—
521C2×C4C23×C3×D311yescharacteristic
522C8—22no—
523C8—62no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—24no—
528C2×C3—64no—
529C2×C3#480914yesdirect product factor
530C2×C3C3×#45114yescomplemented
531C2×C3C2×#88211yescharacteristic
532C2×C3C2×#91511yescharacteristic
533C2×C3C2×D3×Q1611yescharacteristic
534C2×C3C2×C3×#12011yescharacteristic
535C2×C3C22×C3×Q1611yescharacteristic
536C2×C3C2×C3×#13711yescharacteristic
537D3—24no—
538C22—34no—
539C22—62no—
540C22—62no—
541C22—68no—
542C22C3×#88212yes—
543C22C3×#91512yes—
544C22C3×D3×Q1612yes—
545C22C2×C3×D3×D411yescharacteristic
546C4—24no—
547C4—42no—
548C4—62no—
549C4—64no—
550C4—122no—
551C4C3×#88212yes—
552C4C22×C3×D1211yescharacteristic
553C4C2×C3×D3×D411yescharacteristic
554C3—21no—
555C3C2×#480911yescharacteristic, direct product factor
556C3C2×C3×#45111yescharacteristic, complemented
557C2—64no—
558C2C3×#480914yesdirect product factor
559C2C2×C3×#88211yescharacteristic
560C2C2×C3×#91511yescharacteristic
561C2C2×C3×D3×Q1611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C3×#103D3
hypocenterC3C2×C3×#451
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
3. C22×C3×Dic12C2semidirect
5. C2×C32×#103C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4809C2direct (N × H)
10. C2×#4809C3direct (N × H)
24. C2×C3×#216C22semidirect
29. C2×C3×Dic12C22semidirect
32. C32×#103C22semidirect
34. C3×#810C22semidirect
40. C22×#216C2×C3semidirect
41. C22×Dic12C2×C3semidirect
46. C2×C3×#103D3semidirect
47. C2×C3×#103C2×C3semidirect
50. C2×#810C2×C3semidirect
51. #4809C2×C3direct (N × H)
130. C2×#216C22×C3semidirect
135. C2×Dic12C22×C3semidirect
140. C3×#103C2×D3semidirect
141. C3×#103C22×C3semidirect
144. #810C22×C3semidirect
148. C22×C3×D3Q16semidirect
186. C2×#103C3×D3semidirect
286. C2×C3×D3C2×Q16semidirect
317. #103C2×C3×D3semidirect
328. C22×D3C3×Q16semidirect
402. C2×C32#451semidirect
466. C2×D3C2×C3×Q16semidirect
488. C32C2×#451semidirect
529. C2×C3#4809direct (N × H)
530. C2×C3C3×#451semidirect
555. C3C2×#4809direct (N × H)
556. C3C2×C3×#451semidirect
558. C2C3×#4809direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×D3×Q82
C22×C3×#2162
C22×C3×Dic122
C2×C3×#8972
C2×C32×#1032
C2×C3×(C2×D3)⋊C82
C2×C3×#8102
C3×#48092
C2×C3×#4513
C2×#48093